document.write( "Question 334146: log[4](3x+1)=2 \n" ); document.write( "

Algebra.Com's Answer #239431 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%284%2C+%283x%2B1%29%29+=+2\"$
\n" ); document.write( "When the equation is logarithmic and the variable you are solving for is in the argument of the logarithm, the key is to rewrite the logarithmic equation in exponential form:
\n" ); document.write( " $\"4%5E2+=+3x%2B1\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"16+=+3x+%2B+1\"$
\n" ); document.write( "This is now a very simple equation to solve:
\n" ); document.write( " $\"15+=+3x\"$
\n" ); document.write( " $\"5+=+x\"$
\n" ); document.write( "With any logarithmic equation you should check your answers. You must ensure that no arguments of any logarithms become zero or negative!

\n" ); document.write( "Checking x = 5 in the original equation:
\n" ); document.write( " $\"log%284%2C+%283x%2B1%29%29+=+2\"$
\n" ); document.write( " $\"log%284%2C+%283%285%29%2B1%29%29+=+2\"$
\n" ); document.write( " $\"log%284%2C+%2815%2B1%29%29+=+2\"$
\n" ); document.write( " $\"log%284%2C+%2816%29%29+=+2\"$
\n" ); document.write( "The argument is positive to the solution checks! \n" ); document.write( "

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